Method of overnight closed-loop insulin delivery with model predictive control and glucose measurement error model

ABSTRACT

A closed-loop method for insulin infusion overnight uses a model predictive control algorithm (“MPC”). Used with the MPC is a glucose measurement error model which was derived from actual glucose sensor error data. That sensor error data included both a sensor artifacts component, including dropouts, and a persistent error component, including calibration error, all of which was obtained experimentally from living subjects. The MPC algorithm advised on insulin infusion every fifteen minutes. Sensor glucose input to the MPC was obtained by combining model-calculated, noise-free interstitial glucose with experimentally-derived transient and persistent sensor artifacts associated with the FreeStyle Navigator® Continuous Glucose Monitor System (“FSN”). The incidence of severe and significant hypoglycemia reduced 2300- and 200-fold, respectively, during simulated overnight closed-loop control with the MPC algorithm using the glucose measurement error model suggesting that the continuous glucose monitoring technologies facilitate safe closed-loop insulin delivery.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of U.S. Application No. 61/165,467,filed Mar. 31, 2009; and 61/173,133, filed Apr. 27, 2009; and61/248,353, filed Oct. 2, 2009, all of which are incorporated byreference in their entirety.

BACKGROUND

The invention is generally directed to an integrated system of bloodglucose level detection and use of that information in setting insulindelivery parameters, and more particularly, to the use of actual sensordata in characterizing a sensor for use in performing pre-clinicalclosed-loop trial studies in silico.

Diabetes is a metabolic disorder that afflicts tens of millions ofpeople throughout the world. Diabetes results from the inability of thebody to properly utilize and metabolize carbohydrates, particularlyglucose. Normally, the finely-tuned balance between glucose in the bloodand glucose in bodily tissue cells is maintained by insulin, a hormoneproduced by the pancreas which controls, among other things, thetransfer of glucose from blood into body tissue cells. Upsetting thisbalance causes many complications and pathologies including heartdisease, coronary and peripheral artery sclerosis, peripheralneuropathies, retinal damage, cataracts, hypertension, coma, and deathfrom hypoglycemic shock.

In patients with insulin-dependent diabetes, the symptoms of the diseasecan be controlled by administering additional insulin (or other agentsthat have similar effects) by injection or by external or implantableinsulin pumps. The “correct” insulin dosage is a function of the levelof glucose in the blood. Ideally, insulin administration should becontinuously readjusted in response to changes in blood glucose level.In diabetes management, “insulin” instructs the body's cells to take inglucose from the blood. “Glucagon” acts opposite to insulin, and causesthe liver to release glucose into the blood stream. The “basal rate” isthe rate of continuous supply of insulin provided by an insulin deliverydevice (pump). The “bolus” is the specific amount of insulin that isgiven to raise blood concentration of the insulin to an effective levelwhen needed (as opposed to continuous).

Presently, systems are available for continuously monitoring bloodglucose levels by implanting a glucose sensitive probe into the patient.Such probes measure various properties of blood or other tissues,including optical absorption, electrochemical potential, and enzymaticproducts. The output of such sensors can be communicated to a hand helddevice that is used to calculate an appropriate dosage of insulin to bedelivered into the blood stream in view of several factors, such as apatient's present glucose level, insulin usage rate, carbohydratesconsumed or to be consumed, and exercise, among others. Thesecalculations can then be used to control a pump that delivers theinsulin, either at a controlled basal rate, or as a bolus. When providedas an integrated system, the continuous glucose monitor, controller, andpump work together to provide continuous glucose monitoring and insulinpump control.

Such systems at present require intervention by a patient to calculateand control the amount of insulin to be delivered. However, there may beperiods when the patient is not able to adjust insulin delivery. Forexample, when the patient is sleeping, he or she cannot intervene in thedelivery of insulin, yet control of a patient's glucose level is stillnecessary. A system capable of integrating and automating the functionsof glucose monitoring and controlled insulin delivery would be useful inassisting patients in maintaining their glucose levels, especiallyduring periods of the day when they are unable to intervene.

Since the year 2000, at least five continuous or semi-continuous glucosemonitors have received regulatory approval.¹ In combination withcontinuous subcutaneous insulin infusion (“CSII”),² these devices havepromoted research toward closed-loop systems, which deliver insulinaccording to real-time needs, as opposed to open-loop systems which lackthe real-time responsiveness to changing glucose levels. A closed-loopsystem, also called the “artificial pancreas,” consists of threecomponents: a glucose monitoring device such as a continuous glucosemonitor (“CGM”) that measures subcutaneous glucose concentration (“SC”);a titrating algorithm to compute the amount of analyte such as insulinand/or glucagon to be delivered; and one or more analyte pumps todeliver computed analyte doses subcutaneously. So far, only a fewprototypes have been developed, and testing has been confined toclinical settings.³⁻⁸ However, an aggressive concerted effort promisesaccelerated progress toward home testing of closed-loop systems.

The development, evaluation, and testing of closed-loop systems aretime-consuming, costly, and confounded by ethical and regulatory issues.Apart from early stage testing in animals such as the dog^(9,10) or theswine,¹¹ testing in the computer (virtual) environment, also termed insilico testing, is the only other alternative to evaluate and optimizecontrol algorithms outside human studies. Chassin and colleagues havedeveloped a simulation environment and testing methodologyl¹² using aglucoregulatory model developed in a multitracer studyl¹³ and evaluateda glucose controller developed within the Adicol Project.¹⁴ Anothersimulator has been reported by Cobelli and associates,¹⁵ building onmodel-independent quantification of glucose fluxes occurring during ameal.¹⁶ The latter simulator has been accepted by the U.S. Food and DrugAdministration to replace animal testing. Patek and coworkers providedguidelines for preclinical testing of control algorithms.¹⁷

However, such simulations have used mathematical models of glucosesensors in which random data is used for simulating errors of thesensor. Random number generators are used to simulate random errors ofsuch sensors based on noise of the sensor. Such data are therefore notbased on the actual performance of any particular sensor and are likelyto have a significant level of inaccuracy.

Closed-loop systems may revolutionize management of type 1 diabetesmellitus (“T1DM”), but their introduction is likely to be gradual,starting from simpler applications such as hypoglycemia prevention orovernight glucose control and progressing to more complex approachessuch as twenty-four hours per day/seven days per week (24/7) glucosecontrol.⁸ The main reason for gradual deployment is the uncertain riskof hypoglycemia and hyperglycemia, which may arise due to (1) intrinsicoverdosing and underdosing of insulin by a control algorithm, and (2)persistent and transient differences between plasma glucose (“PG”) andsensor glucose (“SG”). The transient differences could be either ofphysiological origin (SC glucose kinetics) or due to a temporal CGMdevice artifact. The persistent differences result from the CGMcalibration error (“CE”). The relatively slow absorption ofsubcutaneously administered “rapid-acting” insulin analogues and othersystem imperfections such as pump delivery errors may exacerbate thehypoglycemia and hyperglycemia risks.

Hence, those of skill in the art have recognized a need for anintegrated, automated system combining continuous glucose monitoring andcontrolled insulin delivery. Such a system would include variousfeatures to insure the accuracy of the glucose monitor and to protectthe user from either under- or over-dosage of insulin. The system wouldinclude various functions for improving the accuracy, usability,control, and safety of the system, including a variety of alarms whichcould be set by a user or a technician to avoid false alarms whileensuring adequate sensitivity to protect the user. Those skilled in theart have also recognized a need for a more accurate glucose measurementerror model for increasing the accuracy of closed-loop systems. Thepresent invention fulfills these, and other needs.

SUMMARY OF THE INVENTION

Briefly and in general terms, the present invention is directed to asystem for the delivery of insulin to a patient, the system comprising aglucose sensor configured to provide a sensor glucose measurement signalrepresentative of sensed glucose, an insulin delivery device configuredto deliver insulin to a patient in response to control signals, and acontroller programmed to receive the sensor glucose measurement signaland to provide a delivery control signal to the delivery device as afunction of the received sensor glucose measurement signal in accordancewith a control model and a glucose measurement error model, wherein theglucose measurement error model is derived from actual glucose sensormeasurement data.

In more detailed aspects, the glucose measurement error model is derivedsolely from actual glucose sensor measurement data. In another aspect,the glucose measurement error model is derived solely from actualglucose sensor error data, excluding sensor noise data. In anotheraspect, the glucose measurement error model is derived solely fromactual glucose sensor measurement data to the exclusion ofrandomly-generated variable data. In yet a further aspect, the glucosemeasurement error model is derived solely from a fixed time history oferror data from actual use of a glucose sensor of the same type as thesensor of the system. And in yet another aspect, the glucose measurementerror model is derived from actual glucose sensor measurement data froma glucose sensor of the same type as the sensor of the system.

In more detailed aspects, the control model comprises a model predictivecontrol and the controller is also programmed to provide the deliverycontrol signals to the delivery device as a function of a modelpredictive control. The glucose measurement error model is derived fromcalibration error of the glucose sensor, which comprises the differencebetween a plasma glucose level and the sensor glucose level signal ofthe glucose sensor. Further, the glucose measurement error model isderived from a glucose sensor dropout reading.

In other aspects, the controller is further programmed to recalibratethe system when the difference between the received sensor glucose levelsignal and a plasma glucose level exceeds a predetermined level. Thedelivery control signal is also a function of the weight of a patient, atotal daily insulin dose, and a basal insulin profile, and wherein thecontroller is also programmed to calculate from the control model anaccepted value, the controller is also programmed to calculate from theglucose level signal an inferred value, the controller is alsoprogrammed to forecast a future plasma glucose level excursion based onthe accepted value and inferred value, and the controller is alsoprogrammed to adjust the delivery control signal in accordance with theforecast future plasma glucose level excursion. In more detailedaspects, the accepted value comprises an insulin sensitivity of thepatient, a glucose distribution volume, and an insulin distributionvolume, and the inferred value comprises glucose flux and a carbohydratebioavailability.

In yet further aspects, the controller is also programmed to adjust avalue of the delivery control signal in accordance with a safety check.Such safety check comprises at least one of imposing a maximum infusionrate related to a basal rate depending on a current sensor glucoselevel, time since a previous meal, and carbohydrate content of a meal,shutting off insulin delivery at a predetermined low sensor glucosevalue, reducing insulin delivery when sensor glucose is decreasingrapidly, and capping the insulin infusion to a pre-programmed basal rateif an insulin delivery pump occlusion is inferred.

In another aspect, the glucose sensor, the insulin delivery device, andthe controller are virtual devices, each being programmed for in silicotesting of a system for delivery of insulin to a virtual patient.

The invention is also directed to a method for delivering insulin to apatient, the method comprising sensing a glucose level and providing aglucose measurement signal representative of the sensed glucose,providing a control signal as a function of the glucose measurementsignal in accordance with a control model and a glucose measurementerror model, wherein the glucose measurement error model is derived fromactual/experimental glucose sensor data, and delivering insulin inresponse to the control signal. In a more detailed aspect, providing thecontrol signal further comprises producing the control signal inaccordance with a model predictive control.

In more detailed aspects, the glucose measurement error model used inthe method is derived solely from actual glucose sensor measurementdata. In another aspect, the glucose measurement error model is derivedsolely from actual glucose sensor error data, excluding sensor noisedata. In another aspect, the glucose measurement error model is derivedsolely from actual glucose sensor measurement data to the exclusion ofrandomly-generated variable data. In yet a further aspect, the glucosemeasurement error model is derived solely from a fixed time history oferror data from actual use of a glucose sensor of the same type as thesensor of the system. And in yet another aspect, the glucose measurementerror model is derived from actual glucose sensor measurement data froma glucose sensor of the same type as the sensor of the system.

Further, more detailed aspects include determining a calibration errorof a glucose sensor from actual sensor data, based on the differencebetween a plasma glucose level and the glucose level signal and derivingthe glucose measurement error model therefrom. Deriving the glucosemeasurement error model further comprises determining a glucose sensordropout reading from actual sensor data and deriving the glucosemeasurement error model therefrom.

Other aspects include providing the control signal as a function of theweight of a patient, a total daily insulin dose, and a basal insulinprofile, the method further comprising determining, based on the controlmodel, at least one accepted value, calculating from the glucose levelsignal at least one inferred value, adjusting the control model inaccordance with the accepted value and inferred value, and forecasting afuture plasma glucose level excursion based on the control model.Determining the accepted value comprises basing the determination on aninsulin sensitivity of the patient, a glucose distribution volume, andan insulin distribution volume. Calculating the inferred value comprisescalculating the inferred value also from glucose flux and a carbohydratebioavailability.

In yet further aspects, the method further comprises adjusting a valueof the control signal in accordance with a safety check, comprising atleast one of imposing a maximum infusion rate related to a basal ratedepending on a current sensor glucose level, time since a previous meal,and carbohydrate content of a meal, shutting off insulin delivery at asensor glucose of 77 mg/dl, reducing insulin delivery when sensorglucose is decreasing rapidly, and capping the insulin infusion to apre-programmed basal rate if an insulin delivery pump occlusion isinferred.

In another aspect, the sensing, providing a control signal, anddelivering insulin are performed virtually, each occurring for in silicotesting of a method for delivery of insulin to a virtual patient.

The features and advantages of the invention will be more readilyunderstood from the following detailed description that should be readin conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE TABLES AND DRAWINGS

TABLE 1 provides demographic data of young subjects with type 1 diabetesmellitus participating in studies;

TABLE 2 shows the incidence of severe hypoglycemia per 100 person yearsduring simulated overnight closed-loop studies at increasing levels ofCGM system calibration error;

TABLE 3 shows the incidence of hypoglycemia and hyperglycemia per 100person years during simulated overnight closed-loop studies and duringovernight open-loop studies;

FIG. 1A presents a block diagram of a closed-loop insulin infusionsystem using a model predictive controller;

FIG. 1B presents a block diagram of a closed-loop insulin infusionsystem using a glucose measurement error model in accordance withaspects of the invention;

FIG. 2 shows simulated sensor glucose traces from the four quartiles ofdropout severity alongside the underlying plasma glucose trace. Q1represents negligible dropouts while Q4 represents the most severedropouts;

FIG. 3 provides a protocol of a simulated overnight closed-loop studyshowing a simulated study of fifteen hours duration, starting at 17:00and ending at 08:00 the next day;

FIG. 4 shows a sample simulation of overnight closed-loop controladopting a +20% CGM system calibration error and a dropout trace fromquartile two. The graph presents plasma glucose, interstitial glucose,sensor glucose, and insulin infusion;

FIG. 5 is a graph showing plasma glucose and sensor glucose (median[interquartile range]; N=720 at each level) during simulated overnightclosed-loop studies at different levels of CGM system calibrationerrors, The CGM system calibration error probability distributionfunction is also shown;

FIG. 6 is a chart showing time spent in the glucose target range (80 to145 mg/dl) as quantified using plasma glucose and sensor glucose (medial[interquartile range]; N=720 at each level) during simulated overnightclosed-loop studies at different levels of CGM system calibration error.The CGM system calibration error distribution function is also shown;

FIG. 7 presents the incidence of severe hypoglycemia (≦36 mg/dl) twentyminutes or shorter and longer than twenty minutes during simulatedovernight closed-loop studies as a function of CGM system calibrationerror. At each level of CGM system calibration error, 720 simulationswere run; the occurrence of one event in 720 simulations corresponds toaround fifty events per one-hundred person years;

FIG. 8 presents the incidence of significant hypoglycemia (≦45 mg/dl)sixty minutes or shorter and longer than sixty minutes during simulatedovernight closed-loop studies as a function of CGM system calibrationerror. At each level of CGM system calibration error, 720 simulationswere run; the occurrence of one event in 720 simulations corresponds toaround fifty events per one-hundred person years;

FIG. 9 plots the incidence of significant hyperglycemia (>300 mg/dl)sixty minutes or shorter and longer than sixty minutes during simulatedovernight closed-loop studies as a function of CGM system calibrationerror. At each level of CGM system calibration error, 720 simulationswere run; the occurrence of one event in 720 simulations corresponds toaround fifty events per one-hundred person years; and

FIG. 10 provides a sample simulation showing hypoglycemia due toprandial insulin overdosing.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Referring now in more detail to the exemplary drawings for purposes ofillustrating embodiments of the invention, wherein like referencenumerals designate corresponding or like elements among the severalviews, there is shown in FIG. 1A a basic block diagram of a closed-loopsystem 20 for continuous glucose monitoring and for continuoussubcutaneous insulin infusion using a model predictive controller 26.The patient receives exogenous inputs, such as meals. The patient'sglucose is measured 24, evaluated by the model predictive controller(MPC) and is used by the MPC to control a delivery device, such as apump 28, to deliver medication to the patient to control blood glucose.

Glucose Control Algorithm

Referring now to FIG. 1B, a control algorithm was used based on themodel predictive control (“MPC”) paradigm¹⁸ to deliver insulin in aclosed-loop fashion. Interstitial glucose measurement occurs and everyfifteen minutes, simulated real-time sensor glucose (“SG”) 24 was fedinto the MPC controller 26, which calculated subcutaneous glucoseconcentration (“SC”) insulin infusion for the insulin pump 28. A dosecalculator 45 is included in this embodiment. The MPC controller 26adopts a compartment model of glucose kinetics describing the effect of(1) SC rapid-acting insulin analogue and (2) the carbohydrate (“CHO”)content of meals on SG excursions. A list of abbreviations used in thespecification and drawings and the items they stand for is included atthe end of the specification.

The glucoregulatory model is initialized using a subject's weight, totaldaily insulin dose, and the basal insulin profile (patient parameters)40. These values feed into estimates of temporal insulin sensitivity andglucose and insulin distribution volumes. Using a Kalman filter 46approach, real-time SG measurements are used to update two modelparameters: (1) a glucose flux quantifying model misspecification; and(2) CHO bioavailability. Several competing models differing in the rateof SC insulin absorption and action and the CHO absorption profile arerun in parallel. A computationally efficient, stochastic-based approachis used to derive a combined control model 30 that best explainsobserved SG excursions.¹⁹

Following estimation of model parameters, the combined control model 30is used to forecast plasma glucose (“PG”) 42 excursions over a two andone-half hour prediction horizon. A sequence of standard deviation(“SD”) insulin infusion rates is determined, which approximates thedesired PG trajectory, characterized by a slow decline fromhyperglycemia and a rapid recovery from hypoglycemia to target glucose,which is set at minimum to 104 mg/dl but is elevated up to 132 mg/dl totake into account inaccuracies of model-based predictions. The firstinfusion rate from the sequence of SC insulin infusion rates isdelivered by the insulin pump 28 subject to safety checks 44, which canreduce the infusion rate to prevent insulin overdosing. These checksinclude: (1) imposing a maximum infusion rate of two to five times thepre-programmed basal rate, depending on the current SG level, the timesince the previous meal(s), and CHO content of meal(s); (2) shutting offinsulin delivery at a SG of 77 mg/dl; (3) reducing insulin delivery whenSG is decreasing rapidly; and (iv) capping the insulin infusion to thepreprogrammed basal rate if a pump occlusion is inferred by the MPC26.²²

For the purposes of the present study, MPC algorithm Version 0.02.02 wasused. Earlier versions of the algorithm were used in clinical studiesfor overnight closed-loop insulin delivery in children and adolescentswith T1DM.²⁰⁻²²

Simulation Environment

A simulation environment designed to support the development ofclosed-loop insulin delivery systems was used.¹² The simulationenvironment is flexible and allows the following components to bedefined: a model of glucose regulation, an experimental protocol, aglucose sensing model, an insulin pump model, and outcome metrics. Amodel of glucose kinetics and insulin action described by Hovorka andcolleagues.^(14,23) was adopted. Other submodels include the model of SCinsulin kinetics, the model of gut absorption, and the model ofinterstitial glucose (IG) kinetics.^(23,24)

The simulator includes eighteen synthetic subjects (virtual patients)with T1DM defined by eighteen parameter sets, representing the virtualT1DM population. A subset of parameters were estimated from experimentaldata collected in subjects with T1DM,¹⁴ and the remaining parameterswere drawn from informed probability distributions.^(13,23) Theinter-subject variability is addressed through assigning a unique set ofparameter values to each individual synthetic subject. The subjectsvary, for instance, in their insulin sensitivity to glucosedistribution, disposal, and endogenous glucose production.^(14,23) Thevirtual subjects are characterized by their daily insulin requirements(0.35±0.14 U/day/kg), insulin-to-CHO ratio (1.7±1.0 U/10 g CHO), andbody weight (74.9±14.4 kg). Intra-individual variability of thegluco-regulatory system is represented by superimposing oscillations onselected model parameters or adding random inter-occasion variability toparameter values. Sinusoidal oscillations with an amplitude of 5% and athree-hour period were superimposed on nominal values of most modelparameters. Each parameter had a different phase generated randomly froma uniform distribution U [0,3 h]. Bioavailability of ingested CHO ischaracterized by 20% inter-occasion variability.

For the purposes of the present study, the glucose measurement errormodel 48 was derived from experimental data. The SG concentration wasobtained as SG(t)=IG(t)×(1+CE)+D(t) where IG(t) is noise-freeinterstitial glucose (“IG”) concentration calculated by thegluco-regulatory model and normalized such that, at the steady-state, itis identical to PG; CE is FreeStyle Navigator® Continuous GlucoseMonitor System (“FSN”) calibration error (“CE”), and D(t) is the dropouttrace of the FSN. The pump 28 delivery error model was assumed zeromean, uncorrelated, with a constant 5% coefficient of variation for thecontinuous insulin infusion and the insulin bolus. The simulationenvironment is implemented in Matlab® (The Mathworks, Natick, Mass.).

FreeStyle Navigator CGM System—Dropouts

The FreeStyle Navigator® Continuous Glucose Monitor system with TRUstartalgorithm (Abbott Diabetes Care, Alameda, Calif.) was used for thepresent study. The FSN system occasionally exhibits a nonzero-meansignal artifact referred to here as “dropout,” where certain mechanicalperturbation of the sensor results in a momentarily attenuated glucoseconcentration.²⁵

Dropouts were quantified using data from a study where fifty-eightliving subjects with T1DM had simultaneously worn two sensors over thecourse of up to five days.²⁶ Values from the two sensors wornsimultaneously on each subject were paired every minute. The point-wisedifference between the paired glucose readings was computed. To accountfor residual CE, a segment's point-wise difference was normalized bysubtracting the median bias of the segment.

From each pair, only time segments that overlap the night-time periodwere used, resulting in 285 night time segments. Segments withinsufficient data, either due to a sensor starting or sending in themiddle of the night time session or due to missing data, were excluded.In total, ninety-one segments were excluded because they contained lessthan 840 one-minute data points over the 900 minutes night-time sessionspan. As a result, 194 night-time segments were available for simulationpurposes.

The mean absolute difference in each segment was used to quantifydropout severity, and the 194 night-time sessions were separated intofour quartiles. Ten dropout segments were chosen randomly from eachquartile and used in simulation studies. The simulation environment addsthe selected dropout segment onto the modeled IG concentration.Simulated CGM traces incorporating dropout data from each quartile areshown in FIG. 2.

FIG. 2 presents simulated sensor glucose traces from the four quartilesof dropout severity alongside the underlying plasma glucose trace. Thefirst quartile Q1 represents negligible dropouts while the fourthquartile Q4 represents the most servere dropouts.

FreeStyle Navigator CGM System—Calibration Error

The FreeStyle Navigator System calibration error (“CE”) is defined asCE=(SG−IG)/IG. In these simulations, therefore, a +5% CE means that thereported SG value is consistently 1.05 times higher than expected for agiven IG concentration.

The FSN System is designed for five-day wear, with calibrationsnominally scheduled at 1, 2, 10, 24, and 72 hours after sensorinsertion. For the present study, a morning CGM sensor insertion isassumed for the night-time only closed-loop control. Thus, each nighttime, closed-loop session is assumed not to include a scheduledcalibration, allowing CE to remain constant for the duration of thenight session.

One-hundred and sixteen (116) insertions used to generate dropoutsignals in addition to 469 insertions from other studies with livingsubjects were used to generate a distribution of the FSN CE. The sensordata set comprised 248 living subjects with T1DM or type 2 diabetesmellitus (“T2DM”) and were a combination of general sensor wear andin-clinic wear that included periods of specific glucose and insulinchallenges.

As IG and PG are assumed to be identical at the steady state, CE can beapproximated using an alternative definition: CE=(SG−PG)/PG. The CE fora single calibration session was calculated from pairs of SG-referenceglucose values where all the SG values were derived from a singlecalibration and reference glucose used for calibration were excludedfrom the calculations. Unlike the calculation of dropouts, onlyreference glucose values measured from finger sticks using the inbuiltblood glucose meter were used. In addition, the real-time calibration ofSG values used the FSN system with TRUstart algorithm.

Excluding calibration sessions containing less than ten SG-referenceglucose pairs, 585 insertions yielded 1421 calibration sessions. The CEfor each session was computed by comparing the median value of therelative difference between SG and reference glucose, and 1421 FSN CEswere generated using 35,200 SG-reference glucose pairs, yielding anaverage of 25 pairs for every calibration session.

Protocol of Simulation Studies

As shown in FIG. 3, the simulated study was fifteen hours long, startingat 17:00 and ending at 08:00 the next day. Plasma glucose at the startof the simulated study was drawn from a log-normal distribution, with amean of 126 mg/dl constrained to a range from 72 to 180 mg/dl. A mealconsisting of 50 g CHO was planned at 18:00 and was accompanied by aprandial insulin bolus. The insulin infusion rate between 17:00 and21:00 was calculated using the simulation model of a particular virtualsubject assuming steady-state conditions at the start of the experiment.At 21:00, the closed-loop glucose control algorithm took over theinsulin delivery. The insulin infusion rate was calculated every fifteenminutes on the basis of CGM values, which included the dropout and CEcomponents. Closed-loop control continued until the end of the simulatedexperiment at 08:00. Rescue CHOs (15 g CHO) were administered at SGvalues 63 mg/dl (3.5 mmol/liter) or below when confirmed by a PG valueof 63 mg/dl or below, simulating a confirmatory finger stick glucosemeasurement. Correction insulin boluses were not administered athyperglycemia.

The simulation studies were run in batches differing by the level of FSNCE. In total, 25 levels of FSN CEs ranging from −80% to +100% weresimulated. The range covering 0% to 60% error was subdivided into 5%steps. The remaining range was spaced 10% apart. Each of the eighteenvirtual subjects with T1DM was associated with one of forty randomlyselected CGM dropout traces (ten traces from each of the four quartilesof increasing severity). This resulted in 720 different combinations andformed a single simulation batch. Each batch was run with all 25 levelsof FSN CE, totaling 18,000 simulated overnight studies.

Open Loop Studies

Within the Artificial Pancreas Project at Cambridge (“APCam”), seventeenchildren and adolescents with T1DM treated by CSII for at least threemonths participated in the APCam01 study (monitoring study) and APCam03(exercise study) conducted at the Wellcome Trust Clinical ResearchCentre, Addenbrooke's Hospital, University of Cambridge, UK. Informedconsent was obtained from all study participants or their caregivers.The APCam01²⁰ and APCam03²² clinical studies were originally designed tocompare overnight closed-loop control against the standard CSIItreatment. In the present analysis, only results from the CSIIinvestigations are reported. The study protocols were approved by theCambridgeshire 3 Ethics Committee. The subjects' demographic data areshown in TABLE 1. Four subjects participated in both studies.

In APCam01, on subject's arrival at the Clinical Research Facility at16:00, a sampling cannula was inserted in a vein of an arm and keptpatent with sodium chloride. At 18:00, the subjects ate a self-selectedmeal (87±23 g CHO) accompanied by prandial insulin (9±5 U; 31%±9% oftotal daily bolus amount) calculated according to the individualinsulin-to-CHO ratio and supplemented by correction dose. Plasma glucosewas determined every fifteen minutes from 17:00 to 08:00 the next day.At least two weeks before the first study, the CSII treatment wasoptimized by a healthcare professional by retrospectively analyzingseventy-two hours of nonreal-time SG data.

In APCam03, at least one week before the study, the subjects attendedthe Clinical Research Facility and a ramped treadmill protocol was usedfor the estimation of the peak VO₂ as an indicator of the maximumexercise effort. As used herein “VO₂” refers to the maximal oxygenuptake, which is widely accepted as a measure of cardiovascular fitnessand maximal aerobic power. Continuous recording of VO₂ withbreath-by-breath sampling was taken during the treadmill test and fortwo minutes during recovery after exercise test termination. Heart ratemonitoring was maintained. On the study day, the subjects arrived at15:00 at the Clinical Research Facility. A sampling cannula was insertedand kept patent with sodium chloride. At 16:00, subjects had a lightmeal chosen from a list of standardized snacks (45±13 g CHO, 12±3 g fat,14±4 g protein) accompanied by prandial bolus (4±2 U). The subjectexercised at 55% VO₂ max on the treadmill from 18:00 until 18:45, with arest from 18:20 to 18:25. During exercise, basal insulin was leftunmodified or was reduced according to individual guidelines. During thenight, the subject's standard insulin pump settings were applied. Plasmaglucose was determined every 15 min from 16:00 to 08:00 the next day. IfPG dropped below 36 mg/dl, GlucoGel© (BBI Healthcare, UK) was given andthe study night terminated.

Data Analysis

Severe and significant hypoglycemia was declared at PG≦36 mg/dl (2.0mmol/liter) and ≦45 mg/dl (2.5 mmol/liter), respectively. These arelevels when cognitive behavioral defenses are compromised.²⁷ Significanthyperglycemia was declared at PG≧300 mg/dl (16.7 mmol/liter).

The empirical probability distribution function of FSN CE was calculatedfrom the 1421 calibration sessions discussed above. During simulatedclosed-loop studies, occurrence and duration of hypoglycemia andhyperglycemia based on the simulated PG trace were recorded from 21:00to 008:00. The probability of hypoglycemia and hyperglycemia eventsoccurring overnight at a given FSN CE is obtained as a product of theprobability, c_(i), of the given FSN CE and the probability of overnighthypoglycemia and hyperglycemia, h_(i), at the given FSN CE. The overallevent probability P is obtained as the sum of these products over the 25levels of FSN CE, i.e., P=Σc_(i)h_(i). For APCam01 and APCam03 studies,the overall event probability is obtained as the number of hypoglycemiaand hyperglycemia events divided by the number of overnight stays. Theoverall incidence is obtained as reciprocal to the overall eventprobability.

During simulated closed-loop studies, mean PG, mean SG, andtime-in-target 80-145 mg/dl were calculated between 20:00 and 08:00 toassess the performance of the MPC algorithm at different levels of FSNCE. Values are shown as mean±standard deviation unless stated otherwise.

Simulated Closed-Loop Studies

A sample simulation study with +20% FSN CE using dropout trace fromquartile two is shown in FIG. 4. Overall, 18,000 simulation studies wereperformed; 720 simulation studies were run for each of the 25 levels ofFSN CE. During simulations, the MPC algorithm was unaware of FSN CE andthe extent of the CGM dropout.

FIG. 5 shows PG and SG values obtained simultaneously during simulationstudies at FSN CEs ranging from −80% to +100%. As expected, increasinglevels of FSN CE result in progressively lower median PG. The MPCalgorithm steps up insulin delivery to limit the increase in SG, unawareof progressively increasing gap between sensor and PG. Employing the SGvalues, the MPC algorithm performs less efficiently at high FSN CE (seeFIG. 6, which plots time-in-target values.) However, employing the PGvalues, the MPC algorithm achieves 60% or higher time-in-target for FSNCE ranging from −20% to +100%.

FIGS. 7 and 8 show the incidence of severe (PG≦36 mg/dl) and significant(PG≦45 mg/dl) hypoglycemia across FSN CE. Severe hypoglycemia did notoccur at FSN CE of 40% or lower. Significant hypoglycemia did not occurat FSN CE of 5% or lower.

TABLE 2 breaks down severe hypoglycemia events according to theirduration, providing more detailed information. The longest duration ofsevere and significant hypoglycemia occurred at the highest 100% FSN CE,lasting for 79 and 178 min, respectively.

FIG. 9 plots the incidence of significant hyperglycemia (PG≧300 mg/dl)for the different levels of FSN CE. Significant hyperglycemia lastingsixty minutes or less was present at most levels of FSN CE, while eventslasting more than sixty minutes occurred when FSN CE was below −40% Thelongest duration of significant hyperglycemia occurred at the −80% FSNCE, lasting for 455 minutes.

FreeStyle Navigator Calibration Error Distribution

The probability distribution of FSN CE generated from 1421 calibrationsessions is shown in FIG. 5 and is replicated in FIG. 6. Approximatelythree-fourths (¾) of the distribution resides within the −10% to +10%range of FSN CE; 35 out of 1421 (2.5% calibration sessions had FSN CE of30% or higher. Approximately the same number of sessions (37 out of1421) had a CE of −30% or lower. FIG. 5 presents plasma glucose and SG(median [interquartile range]; N=720 at each level) during simulatedovernight closed-loop studies at different levels of FSN CE. The FSN CEprobability distribution function is also shown. FIG. 6 presents timespent in the glucose target range (80 to 145 mg/dl) as quantified usingPG and SG (median [interquartile range]; N=720 at each level) duringsimulated overnight closed-loop studies at different levels of FSN CE.The FSN CE probability distribution function is also shown.

FIG. 7 presents the incidence of severe hypoglycemia (≦36 mg/dl) 20 minor shorter and longer than 20 min during simulated overnight closed-loopstudies as a function of FSN CE. At each level of FSN CE, 720simulations were run; occurrence of one event in 720 simulationscorresponds to around 50 events per 100 person years.

FIG. 8 presents the incidence of significant hypoglycemia (≦45 mg/dl) 60min or shorter and longer than 60 min during simulated overnightclosed-loop studies as a function of FSN CE. At each level of FSN CE,720 simulations were run; occurrence of one event in 720 simulationscorresponds to around 50 events per 100 person years.

Open-Loop Studies

During APCam01 and APCam03 studies, PG at 20:00 was 207±97 mg/dl.Average overnight PG from 20:00 to 08:00 was 146±65 mg/dl. Time spent inthe target glucose range from 20:00 to 08:00 was 40% (18-61%) (median[interquartile range]).

During APCam03, one “severe” hypoglycemic event was observed (PG≦36mg/dl). The subject was given GlucoGel®, and the study night wasterminated; thus the duration of the untreated severe hypoglycemic eventcannot be ascertained. Two episodes of “significant” hypoglycemia wereobserved (PG≦45 mg/dl): one study APCam01 over forty-five minutes induration and another in APCam03 over seventy-five minutes in duration,preceding the severe hypoglycemic event above.

Overall Incidence of Hypoglycemia and Hyperglycemia

The overall incident of hypoglycemia and hyperglycemia duringclosed-loop and open-loop studies is shown in TABLE 3.

FIG. 9 presents the incidence of significant hyperglycemia (>300 mg/dl)60 min or shorter and longer than 60 min during simulated overnightclosed-loop studies as a function of FSN CE. At each level of FSN CE,720 simulations were run; occurrence of one event in 720 simulationscorresponds to around 50 events per 100 person years.

DISCUSSION

The present study suggests that overnight closed loop combining an MPCalgorithm and the FSN CGM system is expected to reduce the risk ofhypoglycemia and hyperglycemia compared to the standard CSII therapy.Overnight closed-loop insulin delivery is expected to reduce theincidence of (1) severe hypoglycemia 2300-fold, (2) significanthypoglycemia 200-fold, and (3) significant hyperglycemia 200-fold.

These reductions are indicative rather than conclusive given thedifferences in subject populations; the lower incidence of hypoglycemiaevents, particularly those observed clinically during the CSIItreatment; and uncertainties associated with in silico testing. It isimportant to stress that simulated results need to be verified withclinical data and that efforts should be made to assess truehypoglycemia incidence, which may not be indicated by SG traces alonedue to the possible presence of the kinds of persistent and transientsensing errors described. In addition, as average SG levels may bereduced during closed-loop insulin delivery compared to the standardCSII treatment, the presence of transient errors due to dropouts mayerroneously suggest an increase in hypoglycemic events, i.e., SG maytemporarily drop below the hypoglycemic threshold while PG remains aboutthe threshold.

The incidence calculations are influenced by three main components: 1)the persistent sensing error, 2) the transient sensing error, and 3)insulin misdosing by the control algorithm. In the present study, theassessment of the first two components is based on large observationaldata sets, providing solid foundations for the incidence calculations.The assessment of the last component is addressed by in silico testing.These simulations are the least strong part of our approach due tolimitations of the glucose regulation model but facilitate a rationalway to assess performance of a closed-loop system prior to itsevaluation in larger clinical studies.

It is argued that the persistent sensing error poses a greater risk ofhypoglycemia than the transient sensing error. When SG consistentlyexceed PG levels, the risk of undetected sustained hypoglycemiaincreases; for example, a 100% persistent error translates a PG readingof 50 mg/dl into a SG reading of 100 mg/dl. The persistent errorreflects primarily the SG CE. The present study suggests that severehypoglycemia arises only at an FSN CE of 45% and higher with thestudy-specific MPC algorithm. This represents 0.845% of the calibrationsegments. Thus the characterization of tails of the distribution of theSG CE is essential for the correct quantification of the hypoglycemiarisk, suggesting that risk calculations can only be carried out oncelarge data sets characterizing the performance of any particular CGMsystem are available.

From a closed-loop control perspective, transient errors such asdropouts could trigger a momentary reduction or cessation of insulincommand due to the perceived hypoglycemia event (present or nearfuture). Such a response might increase the risk of hyperglycemia.Closed-loop systems with a strong predictive and/or derivative termmight generate a momentarily exaggerated insulin command when a rapiddropout recovery occurs. If PG is already low, then this transientresponse could increase the risk of hypoglycemia. The effect of dropoutsis illustrated in FIG. 2. Four simulated SG traces with different levelsof dropout severity are shown alongside the underlying PG measurements.

In the present study, the transient error was obtained by taking thedifference of two SG traces and correcting them for CE.Methodologically, this approach overestimates the transient error as, bydefinition, when subtracting two SG traces, the variances of the twotransient errors presented in the component SG traces add up. However, avisual inspection of simultaneously observed SG traces in quartiles twoto four indicates that the transient error in one of the two SG tracestypically dominates, justifying our pragmatic approach, which preservesimportant characteristics such as dropout clustering.

Prior investigation of the validity of the predictions made by in silicotesting increases the confidence in the incidence calculations. Wepreviously validated the virtual population of 18 subjects with T1DM bysimulating a fifteen hour clinical study with an MPC algorithm.²⁸ Theprotocol of the simulated study reflected the APCam01 study conducted intwelve children and adolescents with T1DM.²⁰ Premeal PG during thesimulated study was designed to match that of the real study (177±56versus 171±67 mg/dl, p=not significant (“NS”); unpaired t test). Sensorglucose at the start of closed-loop control (220±72 versus 191±54 mg/dl,p=NS) and mean overnight SG (137±22 versus 141±25 mg/dl, p=NS) weresimilar during simulated and real studies. Time spent in the targetglucose range 80 to 145 mg/dl was not significantly different at 69%(62-78%) versus 63% (49-78%) (median [interquartile range], p=NS).Kovatchev and associates' low blood glucose index [0.5 (0.2-0.9) versus0.3 (0.0-1.0), p=NS] and high blood glucose index [3.4 (1.3-6.8) versus3.7 (0.6-6.8), p=NS]²⁹ were also similar during the real and simulatedstudies, supporting the validity of glucose predictions at low and highglucose levels.

We further assessed the validity of in silico predictions by simulatingopen-loop studies. First, optimum prandial and optimum basal insulin toachieve and maintain PG at 108 mg/dl were determined for the eighteenvirtual subjects during a fifteen hour simulated study commencing at17:00, with a 50 g CHO meal planned at 18:00. Then basal insulin wasincreased by 20% and an identical study design was simulated. Additionalsimulations were performed, with basal insulin increased by 55% and 85%.These increases in the basal insulin delivery corresponded todifferences between the average delivered insulin rate and the averageinsulin rate preprogrammed on the insulin pump during thirty-threeovernight closed-loop studies in young people with T1DM treated byCSII.³⁰ In these thirty-three closed-loop studies, a 20% overestimationof basal insulin was observed in three studies, a 55% overestimation infour studies, and an 85% overestimation in one study.

At the 20% overestimation of basal insulin, the simulations yielded nosevere hypoglycemia and one significant hypoglycemia in the eighteenvirtual subjects. At the 55% overestimation, five and three hypoglycemiaevents were observed. At the 85% overestimation, eight and two eventsoccurred. This indicates the incidence of severe hypoglycemia duringsimulated studies at 1720 per 100 person years, which tallies extremelywell with a corresponding incidence of 1739 per 100 person yearsrecorded during “true” open loop studies (see Table 3). The incidence ofsignificant hypoglycemia during simulations was 1044 per 100 personyears, which is less but still comparable to that observedexperimentally at 3479 per 100 person years; the difference in theincidence rates corresponds to two significant hypoglycemia events overthirty-three nights. Overall, these results suggest that in silicosimulations provide acceptable predictions of hypoglycemia incidenceduring open-loop studies, supporting the validity of in silicopredictions during closed-loop studies.

The MPC algorithm used in the present study has important in-builtsafety features. It uses the pre-programmed insulin infusion rate as aninitial estimate of the insulin needed to achieve normoglycemia. If SGincreases, the MPC algorithm controller steps up insulin delivery butdoes so cautiously and at the expense of suboptimal SG levels. This isevident in FIGS. 5 and 6, which demonstrate that, with increasing levelsof FSN CE, the mean SG concentration increases and the time-in-targetassessed with the use of SG decreases. This design feature of the MPCalgorithm reduces the impact of FSN CE on the risk of hypoglycemia.

The simulation study design included a relatively small evening mealcompared to the body weight of the virtual subjects. Additionally,pre-meal PG was constrained to levels between 72 and 180 mg/dl. Incombination, these two study design aspects limit postprandialhyperglycemia excursions, which are expected to be more pronounced afterlarger meal sizes and at elevated premeal PG values. Conversely,prandial insulin overdosing due to overestimation of the meal size mayresult in early postprandial hypoglycemia, which cannot be prevented byclosed-loop insulin delivery even if insulin infusion is stopped. Someof the episodes of hypoglycemia observed in the present study weredirectly attributable to prandial insulin overdosing prior to the startof closed-loop control. An example is shown in FIG. 10, where theinsulin overdelivery is confounded by a +30% FSN CE. Hypoglycemiaoccurred prior to the start of the closed-loop session. Although insulindelivery virtually stopped at the start of closed loop, PG and SGcontinued to decrease for another thirty minutes. The hypoglycemia eventremained undetected, as SG did not reach the hypoglycemia threshold of63 mg/dl.

The use of CGM alone is expected to reduce the hypoglycemia andhyperglycemia risks as observed in the Juvenile Diabetes ResearchFoundation CGM trial.³¹ The observed improvements are clinicallyimportant but lack the scale offered by the overnight closed-loopapproach. However, even the overnight closed-loop approach, the risk ofhypoglycemia and hyperglycemia is not eliminated. The duration ofsignificant and severe hypoglycemia during simulation studies is limitedto one and three hours, which is slightly less than the two to fourhours of SG-documented hypoglycemia that has been reported prior toseizures.

FIG. 10 presents a sample simulation showing hypoglycemia due toprandial insulin overdosing. Prandial insulin accompanied the meal at18:00. The closed loop started at 21:00. Sensor glucose was obtainedusing a +30% FSN CE and a dropout trace from quartile two. Hypoglycemiaoccurred before the start of the closed-loop session and continued toworsen for another thirty minutes after the start of closed loopalthough insulin delivery was virtually turned off. Hypoglycemia wasundetected, as SG did not reach the hypoglycemia threshold of 63 mg/dl.FreeStyle Navigator CE at +30% or higher is estimated to occur 2.5% ofthe time, assuming no recalibration is performed between scheduledcalibrations.

The FSN CE distribution shown in FIGS. 5 and 6 was constructed assumingthat only the five FSN scheduled calibrations are performed. If a manualrecalibration was performed to rectify excessive CEs that would havebeen evident when SG was compared against a finger stick reading, therisk of hypoglycemia and hyperglycemia during overnight closed loopcould be further reduced.

More detailed information about transient and persistent sensing errorsis required to determine if the present results may be transferable toother commercially available CGM systems.³³ Transferability to othercontrol algorithms is uncertain given the wide range of controlapproaches.

In conclusion, overnight closed loop using an MPC algorithm andreal-time glucose sensing by the FSN system may offer a 200-2300-foldreduction of the hypoglycemia and hyperglycemia incidence. This suggeststhat existing continuous glucose sensing technologies facilitate safeclosed-loop insulin delivery, although confirmation in large clinicalstudies is required.

Abbreviation List:

Abbrev. Stands For: A1C hemoglobin A1C APCam Artificial PancreasCambridge BMI body mass index CE calibration error of FreeStyleNavigator System CGM continuous glucose monitoring CHO carbohydrate CLclosed loop CSII continuous subcutaneous insulin infusion dl deciliterD(t) dropout trace of FreeStyle Navigator System FSN FreeStyle NavigatorContinuous Glucose Monitoring System g grams IG interstitial glucose lliter mg/dl milligrams per deciliter MPC model predictive control NS notsignificant OL open loop PG plasma glucose SC subcutaneous glucoseconcentration SD standard deviation SG sensor glucose T1DM type 1diabetes mellitus T2DM type 2 diabetes mellitus VO₂ Maximal oxygenuptake, which is accepted as a measure of cardiovascular fitness andmaximal aerobic power. Also referred to as maximal oxygen consumption,maximal oxygen uptake, or aerobic capacity.

Table 4 includes a list of documents to which reference is made by meansof endnotes in the text above. Each of those documents listed in Table 4is hereby incorporated by reference.

While the invention has been described in connection with what ispresently considered to be the most practical and preferred embodiments,it is to be understood that the invention is not to be limited to thedisclosed embodiments and elements, but, to the contrary, is intended tocover various modifications, combinations of features, equivalentarrangements, and equivalent elements included within the spirit andscope of the appended claims.

1-18. (canceled)
 19. A method for delivering insulin to a patient, themethod comprising: sensing a glucose level and providing a glucosemeasurement signal representative of the sensed glucose; providing acontrol signal as a function of the glucose measurement signal inaccordance with a control model and a glucose measurement error model,wherein the glucose measurement error model is derived from actualglucose sensor measurement data; and delivering insulin in response tothe control signal.
 20. The method for delivering insulin of claim 19,wherein the glucose measurement error model is derived solely fromactual glucose sensor measurement data
 21. The method for deliveringinsulin of claim 19, wherein the glucose measurement error model isderived solely from actual glucose sensor error data, excluding sensornoise data.
 22. The method for delivering insulin of claim 19, whereinthe glucose measurement error model is derived solely from actualglucose sensor measurement data to the exclusion of randomly-generatedvariable data.
 23. The method for delivering insulin of claim 19,wherein the glucose measurement error model is derived solely from afixed time history of error data from actual use of a glucose sensor ofthe same type as the sensor of the system.
 24. The method for deliveringinsulin of claim 19, wherein the glucose measurement error model isderived from actual glucose sensor measurement data from a glucosesensor of the same type as the sensor of the system.
 25. The method fordelivering insulin of claim 19, wherein the glucose measurement errormodel is derived solely from a fixed time history of error data fromactual use of a glucose sensor of the same type as the sensor of thesystem, to the exclusion of randomly-generated variable data and to theexclusion of sensor noise data.
 26. The method for delivering insulin ofclaim 19, wherein providing the control signal further comprisesproducing the control signal in accordance with a model predictivecontrol.
 27. The method for delivering insulin of claim 19, furthercomprising determining a calibration error of a glucose sensor fromactual sensor data and deriving the glucose measurement error modeltherefrom.
 28. The method for delivering insulin of claim 27, whereindetermining a calibration error comprises determining calibration errorbased on the difference between a plasma glucose level and the glucoselevel signal.
 29. The method for delivering insulin of claim 19, furthercomprising determining a glucose sensor dropout reading from actualsensor data and deriving the glucose measurement error model therefrom.30. The method for delivering insulin of claim 19, wherein providing thecontrol signal is also a function of weight of a patient, a total dailyinsulin dose, and a basal insulin profile, the method furthercomprising: determining, based on the control model, at least oneaccepted value; calculating from the glucose level signal at least oneinferred value; adjusting the control model in accordance with theaccepted value and inferred value; and forecasting a future plasmaglucose level excursion based on the control model.
 31. The method fordelivering insulin of claim 30, wherein determining the accepted valuecomprises basing the determination on an insulin sensitivity of thepatient, a glucose distribution volume, and an insulin distributionvolume.
 32. The method for delivering insulin of claim 30, whereincalculating the inferred value comprises calculating the inferred valuealso from glucose flux and a carbohydrate bioavailability.
 33. Themethod for delivering insulin of claim 19, further comprising adjustinga value of the control signal in accordance with a safety check.
 34. Themethod for delivering insulin of claim 33 wherein adjusting a value ofthe control signal comprises at least one of: imposing a maximuminfusion rate related to a basal rate depending on a current sensorglucose level, time since a previous meal, and carbohydrate content of ameal; shutting off insulin delivery at a predetermined low sensorglucose value; reducing insulin delivery when sensor glucose isdecreasing rapidly; and capping the insulin infusion to a pre-programmedbasal rate if an insulin delivery pump occlusion is inferred.
 35. Themethod for delivering insulin of claim 19, wherein sensing, providing acontrol signal, and delivering insulin are performed virtually, eachoccurring for in silico testing of a method for delivery of insulin to avirtual patient.